Modeling of electrical circuits using symbolic analysis based on a circuit's topology in order to obtain symbolic expressions of circuit parameters is known in the art. Although such modeling allows for fast model creation and simulation to produce predictive analyzable equations, it is not well suited for modeling nonlinear circuits. Further, if very good accuracy is required, the resulting symbolic expressions can become impossible to interpret.
Numerical analysis of electrical circuits is also well known in the art. This approach solves circuit equations extracted from a circuit's topology for a given set of conditions. The resulting output pertains to operating points of the circuit in question and/or to numerical waveforms. Although such approaches work for linear and nonlinear circuits alike, are easy to set-up and accurate, they don't produce any behavior model of the circuit and offer little insight to circuit designers.
Nonlinear regression analysis of electrical circuits is another known approach to modeling. This approach requires extensive simulation of the circuit for different circuit parameter values and the generation of a black box model such as, for example, a neural network model. Although this type of approach works for arbitrary nonlinear circuits, allows for fast model simulation, and can be accurate, the model creation is time-consuming and the approach itself does not produce symbolic expressions.
Another known approach to circuit modeling is that of symbolic modeling using templates for the symbolic expressions used in describing characteristics of a given circuit. This approach requires extensive simulation of the circuit for different circuit parameter values and the generation of a model based on a functional template. An instance of such an approach uses posynomials in its functional template. Such an approach provides symbolic expressions, works for arbitrary nonlinear circuits, allows for fast simulation and can be somewhat accurate. However, questions remain as how to choose the template. Further, in addition to the time-consuming task of model creation, the accuracy of posynomial-based models can be poor and the resulting expressions are too big to be interpretable.
The approaches described above deal mainly with modeling static models of electrical circuits. However, several approaches in modeling the dynamic behavior of electrical circuits are also known. Such approaches include manual behavior model design, Model Order Reduction, numerical simulation and nonlinear regressions. Creating such models can take weeks to years and even then, a model's validity can become obsolete as new technologies emerge.
It is, therefore, desirable to provide a circuit modeling approach that produces symbolic expressions of circuit parameters that are interpretable, accurate and adaptable to emerging technologies.